#### Logic

- If A is married and looks at B and B looks at C who is unmarried, is a married person looking at an unmarried person?

yes

no

can’t tell

## Solution

*Yes*

*Whether B is married or unmarried a married person is looking at an unmarried person*

- You have 3 coins. 1 weighs less than the rest. Can you find it with just 1 weighing?
- Divide the three coins into two groups of one coin each, and leave the third coin aside.
- Place one coin on each side of the balance scale.
**If the scale balances**, then neither of the two coins on the scale is the lighter one, meaning the coin you left aside is the lighter coin.**If the scale does not balance**, the side that goes up (the lighter side) contains the lighter coin.

## Solution

To find the lighter coin among the three coins with just one weighing, you can use a balance scale and follow these steps:

There are two possible outcomes from this weighing:

This method ensures you can identify the lighter coin among the three with just one use of the scale.

- 10 red socks, 10 blue socks. How many to pull for matching pair? How many to pull for 1 of each?

## Solution

3 and 11 respectively

- If you have 3 you have 3, if you have 2 you have 2, if you have 1 you have none. What is it?

## Solution

Choice

#### Arithmetic

- Dinner cost $60 including a 20% tip. How much was the meal?

## Solution

1.2x = 60

x = 50

- I'm 3x your age today. In 3 years I'll be twice your age. What are our ages?

## Solution

y = 3x

y + 3 = 2(x + 3)

3 and 9

- A bat costs $1 more than a ball. Together they cost $1.10. How much do they each cost?

## Solution

ball = .05, bat = 1.05

- What's bigger the square of an average or the average of the squares?

## Solution

average of the squares

#### Probability & Expected Value

- If 10% of population is left handed and 1% of women are left handed, what percentage of men are left handed? (assume equal amounts of men and women in the population)

## Solution

.5 women are left handed

9.5/10 left handed people must be men

9.5/50 = 19% of men are left handed

**Divisibility Rules**

**Divisibility Rules**

- Divisible by 10 if ends in 0

- Divisible by 2 if even

- Divisible by 3 if digital roots is 3

- Divisible by 4 if the last 2 digits of a number are divisible by 4

- Divisible by 5 if the last digit is divisible by 0 or 5

- Divisible by 6 if it's divisible by 3 and even

- Divisible by 7 if the difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to
**0**

- Divisible by 8 if the last 3 numbers are 000 or last 3 are divisible by 8

- divisible by 9 if digital roots is 9

#### Misc Topics

- Richter scale as log scale. A 6 is 1000x a 3 not 2x

## Cigarette question: A miser can make 1 cigarette from 5 cigarette butts. What is the maximum number of cigarettes the miser can make from 1000 cigarette butts ?

he first makes 1000/5 = 200 cigarettes which gives him 200 butts in the end
then he has 200 butts to make 200/5= 40 cigarettes which gives 40 butts
again he has 40/5 = 8 cigarettes which gives 8 butts
8/5 = 1.6 but he makes only 1 cigarette of that.
3 butts remain in the end - useless (as he cant make a cigarette with 3 butts)
Total cigarettes made = 200 + 40 + 8 +1 = 249 cigarettes

## MAD and daylight savings time

Daylight savings time causes accidents but how do we know?

If CA averages 100 car accidents a day, then would you be surprised if there was 92? 105? 300?

There's an implicit level of “surprise”

Compute MAD by averaging the distances of each day’s accidents from 100. The more a sample exceeds the average the more likely there result is not random

## You drive 1 mile at 30mph, how fast do you have to drive the second mile to average 60 mph for the trip?

Can't be done. The first mile took 2 and to drive 2 miles at 60mph you must complete the trip in 2 min

## Triangle method for summing the numbers from 1 to N

## Do a lesson on arithmetic means, weighted average.

- Do a lesson on compounding

- Do geometric means and show how that is used for multiplied quantities such as growth rates.

- Tie together arithmetic and geometric means and how because they are different it can lead to different strategies and the need to “quarantine” risk

## Expected Value

EV of:

- coin toss game

- Camel Up situation

- Insurance on a iPad

- Roulette wheel

- 2 pointer vs 3 pointer

- Getting a blackjack from a full deck

Next lesson:

Betting odds

## Passphrase stuff

- plotting geometric growth (X^2) vs exponential growth (2^x) and talking about viral growth.

## Sum of finite geometric series

- derivation
- socratically show terms in the sequence
- set equal to the same sequence times
*r* - solve for Sn

## application (via GPT

Real-life examples of summing a finite geometric series include:

**Depreciation**: When an asset depreciates by a constant percentage each year, the total value lost over a number of years can be calculated as the sum of a geometric series.

**Loan Payments**: The formula for calculating the remaining balance of a loan involves a geometric series when the loan is being repaid in equal installments over time.

**Investment Growth**: The total value of an investment over time that receives a constant rate of interest compounded annually can be modeled as a geometric series.

**Electronics**: In a resistor-capacitor (RC) circuit, the voltage across the capacitor or the charging and discharging of the capacitor can be described by a geometric series.

**Computer Science**: In algorithms, particularly divide and conquer algorithms like the binary search, the time complexity can often be expressed as a geometric series.

**Physics**: In certain problems in physics, such as calculating the total distance covered by a bouncing ball where each bounce is a fraction of the height of the previous bounce.

**Acoustics**: Echoes can be thought of as a geometric series, where each successive echo has a smaller amplitude than the previous one

- https://notion.moontowermeta.com/the-cost-of-heating-the-pool

Math questions I do with Zak and excel pool heating https://twitter.com/KrisAbdelmessih/status/1541441470917447681?t=m8rUs6BGe40Bd-Iw1roaww&s=19